Pith Number

pith:QLV4IA7I

pith:2024:QLV4IA7IFDELITKVJKKAWRO65L

not attested not anchored not stored refs pending

An overview of the stability of Sobolev inequalities on Riemannian manifolds with Ricci lower bounds

Francesco Nobili

arxiv:2412.05935 v2 · 2024-12-08 · math.AP · math.DG · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QLV4IA7IFDELITKVJKKAWRO65L}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-07-05T11:34:02.631570Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82ebc403e828c8b44d554a940b45deeac3b3c7bc158a1f66d896366dd8e3b286

Aliases

arxiv: 2412.05935 · arxiv_version: 2412.05935v2 · doi: 10.48550/arxiv.2412.05935 · pith_short_12: QLV4IA7IFDEL · pith_short_16: QLV4IA7IFDELITKV · pith_short_8: QLV4IA7I

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/QLV4IA7IFDELITKVJKKAWRO65L \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 82ebc403e828c8b44d554a940b45deeac3b3c7bc158a1f66d896366dd8e3b286

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a9f0acb5a47f837ac73089e50bba371645eaced0704996d7914c09a68c47fb1",
    "cross_cats_sorted": [
      "math.DG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2024-12-08T13:21:37Z",
    "title_canon_sha256": "f300710992f057adb59ec3230518b6794a94f8a1c72d2cd5538cc42d33fb2ae4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.05935",
    "kind": "arxiv",
    "version": 2
  }
}